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New Semiparametric Estimation Procedure for Functional Coefficient Longitudinal Data Models

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  • Jia Chen
  • Degui Li
  • Yingcun Xia

Abstract

In order to achieve dimension reduction for the nonparametric functional coefficients and improve the estimation efficiency, in this paper we introduce a novel semiparametric estimation procedure which combines a principal component analysis of the functional coefficients and a Cholesky decomposition of the within-subject covariance matrices. Under some regularity conditions, we derive the asymptotic distribution for the proposed semiparametric estimators and show that the efficiency of the estimation of the (principal) functional coefficients can be improved when the within-subject covariance structure is correctly speci ed. Furthermore, we apply two approaches to consistently estimate the Cholesky decomposition, which avoid a possible misspeci cation of the within-subject covariance structure and ensure the efficiency improvement for the estimation of the (principal) functional coefficients. Some numerical studies including Monte Carlo experiments and an empirical application show that the developed semiparametric method works reasonably well in finite samples.

Suggested Citation

  • Jia Chen & Degui Li & Yingcun Xia, 2015. "New Semiparametric Estimation Procedure for Functional Coefficient Longitudinal Data Models," Discussion Papers 15/17, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:15/17
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    More about this item

    Keywords

    Cholesky decomposition; functional coefficients; local linear smoothing; principal component analysis; profile least squares; within-subject covariance;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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